Actually, no, you can ask.
First say something about financial package being an important factor in your decision and ask them under what circumstances, if any, they're willing to reconsider your package. They might engage you right there or they might tell you what you need to do next.
I've heard of the following situations:
* "What? You want more? Hold on......how about $10k more?" (This was on the phone, and I think it was actually a return call the next day, but you get the idea.)
* You need to provide us updated financial info showing your need.
* Everyone who applies is spending big money to do this, so financial need is not a consideration. However, if you believe there are merit-based reasons that you deserve more scholarship money, you may write a letter to the scholarship committee outlining your qualifications. This should be information about you that is not already in your application.
I think situation 3 is the most common. Some board members have been successful in their pleas, and some have not.
I say go ahead and ask - it's not like they're going to revoke the acceptance. As long as you're not a jerk about it, you have nothing to lose. Playing coy is unlikely to get you anywhere.